Multiple Choice
A square loop of wire has a side length of and carries a current. What is the size of its magnetic dipole moment?
28. Magnetic Fields and Forces
Force and Torque on Current Loops
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A single circular loop of wire has a radius of , and carries a current of . What is the maximum torque that could be experienced by this loop due to earth's magnetic field?
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Verified step by step guidance1
First, understand that the torque (τ) experienced by a current-carrying loop in a magnetic field is given by the formula: τ = n * I * A * B * sin(θ), where n is the number of turns (which is 1 for a single loop), I is the current, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the normal to the loop and the magnetic field.
Calculate the area (A) of the circular loop using the formula for the area of a circle: A = π * r^2, where r is the radius of the loop. Given that the radius is 2.0 cm, convert this to meters (0.02 m) before substituting into the formula.
The maximum torque occurs when sin(θ) = 1, which is when the angle θ is 90 degrees. This simplifies the torque formula to τ = I * A * B.
Substitute the given values into the simplified torque formula: I = 4.0 A, A = π * (0.02 m)^2, and B = Earth's magnetic field strength. Note that Earth's magnetic field strength is typically around 25 to 65 microteslas (T), but you may need to use a specific value if provided.
Calculate the torque using the substituted values to find the maximum torque experienced by the loop. Compare your result with the given options to identify the correct answer.
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